Question

Factorise: 6 x2+ 7x -3

Answer 1

• Factoring a quadratic equation can be defined as the process of breaking the equation into the product of its factors.

$\:❏ \: \: \LARGE{\rm{{{\color{orange}{6 {x }^{2} \: + \: 7x \: - 3}}}}}$

• Factorize the equation by breaking down the middle term.

$\large \blue\implies \tt \large \: 6 {x }^{2} \: + \: 7x \: - 3$

• Let’s identify two factors such that their sum is 7 and the product is -18.

Sum of two factors = 7 = 9 - 2

Product of these two factors = 9 × (-2) = 18

• Now, split the middle term.

$\large \blue\implies \tt \large \:6 {x}^{2} \: + \: 9x \: - \: 2x \: - \: 3$

• Take the common terms and simplify.

$\: \\ \large\blue\implies \tt \large \:3x(2x \: + \: 3)\: -1(2x \: + \: 3)$

$\\ \large\blue\implies \tt \large \:(3x \: - \:1 ) \quad \: (2x \: + \: 3) \: = \: 0$

Thus, (3x - 1) and (2x + 3) are the factors of the given quadratic equation.

• Solving these two linear factors, we get

$\large\blue\implies \tt \large \:x \: = \: \frac{1}{3} \: \: , \: \: \frac{ - 3}{2}$

Answer 2

${6x}^{2} + 7x - 3 \\ \\ {6x}^{2} + 9x - 2x - 3 \\ \\ ( {6x}^{2} + 9x) - (2x + 3) \\ \\ 3x(2x + 3) - 1(2x + 3) \\ \\ (3x - 1)(2x + 3).$